Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
148 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 119. C7 | #2103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89896 | 2 |
| #89874 | 2 |
| C7×#341 | 2 |
| C7⋊#338 | 2 |
| #89354 | 2 |
| #89351 | 2 |
| #89347 | 2 |
| #2103 | 7 |